# The Ornstein-Uhlenbeck Semigroup in Bounded and Exterior Lipschitz Domains

Wood, Ian (2009) The Ornstein-Uhlenbeck Semigroup in Bounded and Exterior Lipschitz Domains. In: Janas, Jan and Kurasov, Pavel and Naboko, Serguei and Laptev, Ari and Stolz, Gunter, eds. Methods of Spectral Analysis in Mathematical Physics. Operator Theory: Advances and Applications, 186 . Birkhaeuser, Basel, pp. 415-435. ISBN 978-3-7643-8754-9. (doi:10.1007/978-3-7643-8755-6_21) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:23941)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication) Official URLhttp://dx.doi.org/10.1007/978-3-7643-8755-6_21

## Abstract

We consider bounded Lipschitz domains ? in ? n . It is shown that the Dirichlet-Laplacian generates an analytic C 0-semigroup on L p (?) for p in an interval around 2 and that the corresponding Cauchy problem has the maximal L q -regularity property. We then prove that for bounded or exterior Lipschitz domains Ornstein-Uhlenbeck operators A generate C 0-semigroups in the same p-interval. The method, also allows to determine the domain D(A) of A and, if ? satisfies an outer ball condition, allows to show L p -L q -smoothing properties of the semigroups.

Item Type: Book section 10.1007/978-3-7643-8755-6_21 Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, CalculusQ Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Ian Wood 09 Apr 2010 10:56 UTC 01 Aug 2019 10:33 UTC https://kar.kent.ac.uk/id/eprint/23941 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-7181-7075